Details of the roller chain are shown below. The diagram indicates the inner and outer plate construction with the roller riding on the pins connecting the plates on either side of the chain. The movement of the side plates with respect to the pins causes wear that shows up in the transverse sag of the chain that is illustrated in the photograph. The A chain is an old chain with pin/plate wear and is compared to a new chain, B.

From: Apps, "The Bicycle Book," Smithmark (1993); and Sloane, "Sloane's Complete Book of Bicycling,"
Simon & Schuster (1995)

The nominal length of a complete link in a chain is 1 inch with a chain pitch of half an inch. As the chain wears, the effective length of the link increases. Chain A has worn enough that replacement is appropriate.